Multi-objective optimization for the geometry of trapezoidal corrugated morphing skins

Morphing concepts have great importance for the design of future aircraft as they provide the opportunity for the aircraft to adapt their shape in flight so as to always match the optimal configuration. This enables the aircraft to have a better performance, such as reducing fuel consumption, toxic emissions and noise pollution or increasing the maneuverability of the aircraft. However the requirements of morphing aircraft are conflicting from the structural perspective. For instance the design of a morphing skin is a key issue since it must be stiff to withstand the aerodynamic loads, but flexible to enable the large shape changes. Corrugated sheets have remarkable anisotropic characteristics. As a candidate skin for a morphing wing, they are stiff to withstand the aerodynamic loads and flexible to enable the morphing deformations. This work presents novel insights into the multi-objective optimization of a trapezoidal corrugated core with elastomer coating. The geometric parameters of the coated composite corrugated panels are optimized to minimize the in-plane stiffness and the weight of the skin and to maximize the flexural out-of-plane stiffness of the skin. These objective functions were calculated by use of an equivalent finite element code. The gradient-based aggregate method is selected to solve the optimization problem and is validated by comparing to the GA multi-objective optimization technique. The trend of the optimized objectives and parameters are discussed in detail; for example the optimum corrugation often has the maximum corrugation height. The obtained results provide important insights into the design of morphing corrugated skins

Aircraft control via variable cant-angle winglets

Copyright @ 2008 American Institute of Aeronautics and AstronauticsThis paper investigates a novel method for the control of "morphing" aircraft. The concept consists of a pair of winglets; with adjustable cant angle, independently actuated and mounted at the tips of a baseline flying wing. The general philosophy behind the concept was that for specific flight conditions such as a coordinated turn, the use of two control devices would be sufficient for adequate control. Computations with a vortex lattice model and subsequent wind-tunnel tests demonstrate the viability of the concept, with individual and/or dual winglet deflection producing multi-axis coupled control moments. Comparisons between the experimental and computational results showed reasonable to good agreement, with the major discrepancies thought to be due to wind-tunnel model aeroelastic effects.This work has been supported by a Marie Curie excellence research grant funded by the European Commission

Candidate reduced order models for structural parameter estimation

Introduction Structural parameter estimation is the identification of the physical structural parameters such as mass, damping, and stiffness, or possibly geometric parameters. In practical applications an estimate for these parameters will exist and the estimation process updates these estimates. In linear systems this becomes the estimation of the mass, damping, and stiffness matrices. No papers have been published that directly tackle the major problem of the high model order of theoretical finite element models. This paper argues that in many practical situations reducing the order of a linear model, while maintaining its dependence on unknown parameters, can be beneficial and suggests some order reduction methods. Irrespective of the method used the parameters to be estimated should be carefully selected. Generally the dimension of the measurement vector is considerably smaller than the order of the finite element model. The input to output relationship, even in the absence of noise, could be reproduced by an infinite number of mass, damping, and stiffness matrices. Thus to obtain accurate estimates of physical parameters the choice of which parameters to estimate is important. If mass, damping, and stiffness matrices are available, for example, from a theoretical finite element analysis, then updated matrices "closest" to those of the initial model could be chosen. But even this does not consider the special structure of a typical finite element model. If a homogeneous continuum is discretized then the only unknowns would be the mass, damping, and stiffness properties of the material and the geometry of the modelled item. The elements of the matrices defining the system model will not be independent of each other. In principle it is unreasonable and unnecessary to identify whole mass, damping, and stiffness matrices

The effect of curved tips on the dynamics of composite rotor blades

In this paper, the dynamics of a tailored composite rotating blade with curved tips are investigated, with a view to improving the dynamic behaviour of the blade in flight. The blade tip is curved either in the out-of-plane or in the in-plane directions. The composite blade is modelled by using the exact beam formulation, and the cross-sectional properties of the blade are obtained using the variational asymptotic method. The resulting nonlinear partial differential equations are discretised using a time-space scheme, and the stationary and rotating frequencies of the blade are obtained from the eigenvalues of the linearised system. Three case studies are considered here each of them representing one of the main elastic couplings that might happen in a composite blade. These three elastic couplings are the flap-twist, lag-twist, and extension-twist couplings. All these couplings are very important in the blade design as they can affect the twist and hence the dynamics of the blade. The blade tip length and curvature value are two main parameters that this paper is focused on. It is shown that the curved tip of the blade affects the blade frequencies by adding extra couplings, and therefore could be used as a potential morphing concept for tuning the frequencies, enhancing the aeroelastic stability or performance of the blade in flight

Finite Element Model updating using Hamiltonian Monte Carlo techniques

Abstract: Bayesian techniques have been widely used in finite element model (FEM) updating. The attraction of these techniques is their ability to quantify and characterise the uncertainties associated with dynamic systems. In order to update an FEM, the Bayesian formulation requires the evaluation of the posterior distribution function. For large systems this function is difficult to solve analytically. In such cases the use of sampling techniques often provides a good approximation of this posterior distribution function. The hybrid Monte Carlo (HMC) method is a classic sampling method used to approximate high-dimensional complex problems. However, the acceptance rate (AR) of HMC is sensitive to the system size, as well as to the time step used to evaluate the molecular dynamics (MD) trajectory. The shadow HMC technique (SHMC), which is a modified version of the HMC method, was developed to improve sampling for large-system sizes by drawing from a modified shadow Hamiltonian function. However, the SHMC algorithm performance is limited by the use of a non-separable modified Hamiltonian function. Moreover, two additional parameters are required for the sampling procedure, which could be computationally expensive. To overcome these weaknesses the separable shadow HMC (S2HMC) method has been introduced. This method uses a transformation to a different parameter space to generate samples. In this paper we analyse the application and performance of these algorithms, including the parameters used in each algorithm, their limitations and the effects on model updating. The accuracy and the efficiency of the algorithms are demonstrated by updating the finite element models of two real mechanical structures. It is observed that the S2HMC algorithm has a number of advantages over the other algorithms; for example, the S2HMC algorithm is able to efficiently sample at larger time steps while using fewer parameters than the other algorithms

Asynchronous partial contact motion due to internal resonance in multiple degree-of-freedom rotordynamics

Sudden onset of violent chattering or whirling rotorstator contact motion in rotational machines can cause significant damage in many industrial applications. It is shown that internal resonance can lead to the onset of bouncing-type partial contact motion away from primary resonances. These partial contact limit cycles can involve any two modes of an arbitrarily high degree-of-freedom system, and can be seen as an extension of a synchronisation condition previously reported for a single disc system. The synchronisation formula predicts multiple drivespeeds, corresponding to different forms of mode-locked bouncing orbits. These results are backed up by a brute-force bifurcation analysis which reveals numerical existence of the corresponding family of bouncing orbits at supercritical drivespeeds, provided the dampingis sufficiently low. The numerics reveal many overlapping families of solutions, which leads to significant multi-stability of the response at given drive speeds. Further secondary bifurcations can also occur within each family, altering the nature of the response, and ultimately leading to chaos. It is illustrated how stiffness and damping of the stator have a large effect on the number and nature of the partial contact solutions, illustrating the extreme sensitivity that would be observed in practice

Hyperelastic modelling of post-buckling response in single wall carbon nanotubes under axial compression

AbstractThis paper presents a hyperelastic finite element-based lattice approach for the description of post-buckling response in single wall carbon nanotubes (SWCNTs). A one-term incompressible Ogden-type hyperelastic model is adopted to describe the mechanical response of SWCNTs under axial compression. Numerical experiments are carried out and the results are compared to atomistic simulations, demonstrating the predictive capabilities of the present model in capturing post-buckling behaviour and the main deformation mechanisms under large compressive deformations

Enhancement of harvesting capability of coupled nonlinear energy harvesters through high energy orbits

Mechanical coupling in similar energy harvesters has the potential to enhance their broadband harvesting capability. However, often the performance of one harvester dominates the other, and the coupling transfers energy from the high frequency harvester to the low frequency harvester, thus reducing the capability of the high frequency harvester. Hence, researchers have proposed using the high frequency harvester only as an auxiliary oscillator to save the material cost. This paper investigates the possibility of enhancing the energy harvesting capability of both coupled harvesters. A torsionally coupled electromagnetic pendulum harvester system is considered, which is suitable for low frequency (<5 Hz) applications. The harmonic balance method is used to identify possible multiple solutions, and high magnitude solutions are observed to coexist with low magnitude solutions. These high energy solutions, which are often missed in the numerical simulation, can be attained by a careful choice of initial conditions or energy input. The simulation results show that more energy can be harvested over a wider range of frequencies by ensuring that the response occurs in the high energy orbits. The results show an enhancement of the bandwidth by 54% and 140% for the low and high frequency harvesters, respectively, with the optimum initial conditions. Moreover, an isolated frequency island is reported, which occurs due to the coupling of the nonlinear harvesters